Finite Group Databasebeta

← C2×#13079144 #15623394

Subgroups — C2×#13079144 #15623394

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623031C212yesmaximal
2#13079144C2116yesmaximal, direct product factor
3C2×#10622469C214yesmaximal, complemented
4C2×#10622471C212yesmaximal, complemented
5C2×#10622468C212yesmaximal, complemented
6C2×#10622577C212yesmaximal
7C2×#10622719C211yesmaximal, characteristic
8C2×#10622714C211yesmaximal, characteristic
9C22×C11×#106C211yesmaximal, characteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2212yes—
12C2×#66979C2212yes—
13C2×#66979C2211yescharacteristic
14C2×#66977—24no—
15C22×#4318C2211yescharacteristic
16#10623031—28no—
17#10623031C22116yes—
18C2×#66943—22no—
19C2×#66943C2214yes—
20C2×#66941—22no—
21C2×#66941C2214yes—
22C2×C11×#106C2212yes—
23C2×C11×#106C2212yes—
24C2×C11×#106C2218yes—
25#10622719C2218yes—
26C2×#66882C2212yes—
27C2×#66881C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29#10622714C2218yes—
30C2×#66879C2212yes—
31C2×C8×Dic11C2212yes—
32#10622577C22116yes—
33C2×#66872C2214yes—
34C2×#66871C2214yes—
35#10622471C22116yescomplemented
36#10622469C22132yescomplemented
37#10622468C22116yescomplemented
38C23×C4×C11—22no—
39C23×C4×C11C2311yescharacteristic
40C22×Dic22—24no—
41C22×C8×C11Q818yescomplemented
42C22×C8×C11C2311yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C22×C8×C11C2314yes—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—24no—
47C2×C11×C4⋊C4C2314yes—
48C2×C11×C4⋊C4C2318yes—
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11D412yes—
51#66979—24no—
52#66979D414yes—
53#66979C2318yes—
54#66979C2314yes—
55C2×C4⋊Dic11—24no—
56C2×C4⋊Dic11D412yes—
57C2×C4⋊Dic11C2312yes—
58C2×C4⋊Dic11C2312yes—
59#66977—232no—
60C2×Dic11⋊C4—24no—
61C2×Dic11⋊C4—24no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11C2312yes—
64C2×#4318Q818yescomplemented
65C2×#4318C2314yes—
66C22×C11⋊C8C2312yes—
67#66943—216no—
68#66943—28no—
69#66943C23116yes—
70#66941—216no—
71#66941—28no—
72#66941C23116yes—
73C11×#106C2318yes—
74C11×#106C2318yes—
75#66882C2318yes—
76#66881C2314yes—
77#66881C2314yes—
78#66879C2318yes—
79C8×Dic11C2318yes—
80#66872C23116yes—
81#66871C23116yes—
82C2×#3163—111nomaximal, Sylow
83C24×C11C2×D411yescharacteristic
84C22×C4×C11—24no—
85C22×C4×C11—28no—
86C22×C4×C11—84no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×Q814yes—
90C22×C4×C11C2×Q814yes—
91C22×C4×C11C2411yescharacteristic
92C22×C4×C11C2412yes—
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11C2×D414yes—
96C2×Dic22—216no—
97C2×Dic22—88no—
98C2×C8×C11C2×Q814yes—
99C2×C8×C11C2×Q814yes—
100C2×C8×C11C2×Q8116yescomplemented
101C2×C8×C11C2412yes—
102C2×C8×C11C2412yes—
103C11×C4⋊C4—28no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4C2418yes—
106C22⋊Dic11—28no—
107C22⋊Dic11C2×D418yes—
108C4⋊Dic11—216no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11C2×D418yes—
112C4⋊Dic11C2414yes—
113C4⋊Dic11C2414yes—
114Dic11⋊C4—216no—
115Dic11⋊C4—216no—
116C4×Dic11—28no—
117C4×Dic11C2×D414yes—
118C4×Dic11C2414yes—
119#4318C2×Q8116yescomplemented
120C2×C11⋊C8C2×Q818yes—
121C2×C11⋊C8C2414yes—
122C2×#544—112no—
123#3163—1116no—
124C2×#501—114no—
125C2×#499—112no—
126C2×#498—112no—
127C2×#428—112no—
128C2×#427—111no—
129C22×#106D1111yescharacteristic
130C2×#405—111no—
131C23×C11—24no—
132C23×C11C4⋊Q814yes—
133C23×C11C22×D412yes—
134C23×C11C22×D411yescharacteristic
135C2×C4×C11—28no—
136C2×C4×C11—48no—
137C2×C4×C11—88no—
138C2×C4×C11C4⋊Q818yes—
139C2×C4×C11C4⋊Q814yes—
140C2×C4×C11C22×D412yes—
141C2×C4×C11C22×D411yescharacteristic
142C2×C4×C11C22×Q812yes—
143C2×C4×C11C22×Q814yes—
144C2×C4×C11C22×Q812yes—
145C2×C4×C11C22×Q814yes—
146C2×C4×C11C2511yescharacteristic
147C2×Dic11—28no—
148C2×Dic11—24no—
149C2×Dic11—24no—
150C2×Dic11—44no—
151C2×Dic11—44no—
152C2×Dic11C22×D418yes—
153Dic22—816no—
154C8×C11C22×Q814yes—
155C8×C11C22×Q814yes—
156C11⋊C8C22×Q818yes—
157C22×M16—111no—
158C23×C8C2×D1111yescharacteristic
159#544—1116no—
160#544—228no—
161C2×C4⋊Q8—114no—
162C2×C4⋊Q8—222no—
163C2×#125—114no—
164C2×#125—222no—
165C2×C22⋊Q8—224no—
166C2×#117—111no—
167C2×#117—112no—
168C22×C4⋊C4C2×D1112yes—
169#501—1132no—
170#499—1116no—
171#498—1116no—
172#428—1116no—
173#427—118no—
174C2×#107—112no—
175C2×#107—114no—
176C2×#106—111no—
177C2×#106—111no—
178C2×#106—114no—
179C2×#106C2×D1112yes—
180C2×#106C2×D1112yes—
181C2×#106C2×D1118yes—
182#405—118no—
183C2×#97—112no—
184C2×C4×C8—112no—
185C22×C11—28no—
186C22×C11—24no—
187C22×C11C2×C4⋊Q814yes—
188C22×C11C2×C4⋊Q812yes—
189C22×C11#57714yes—
190C22×C11C23×D411yescharacteristic
191C4×C11—48no—
192C4×C11C2×C4⋊Q814yes—
193C4×C11C2×C4⋊Q812yes—
194C4×C11C23×Q811yescharacteristic
195C4×C11C23×Q811yescharacteristic
196Dic11—28no—
197Dic11—44no—
198Dic11—44no—
199C22×Q8—224no—
200C23×C4—22no—
201C23×C4C22×D1111yescharacteristic
202C2×M16—118no—
203C2×M16—114no—
204C22×C8—112no—
205C22×C8Dic2218yescomplemented
206C22×C8C22×D1111yescharacteristic
207C22×C8C22×D1111yescharacteristic
208C22×C8C22×D1114yes—
209C4⋊Q8—1116no—
210C4⋊Q8—228no—
211C4⋊Q8—2216no—
212#125—1116no—
213#125—228no—
214#125—2216no—
215C22⋊Q8—2232no—
216#117—114no—
217#117—114no—
218#117—118no—
219#117—224no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—112no—
223C2×C4⋊C4—112no—
224C2×C4⋊C4—112no—
225C2×C4⋊C4—224no—
226C2×C4⋊C4—224no—
227C2×C4⋊C4—224no—
228C2×C4⋊C4C22×D1114yes—
229C2×C4⋊C4C22×D1118yes—
230C2×C22⋊C4—112no—
231C2×C22⋊C4—222no—
232C2×C42—112no—
233C2×C42—222no—
234#107—118no—
235#107—1116no—
236#106—114no—
237#106—114no—
238#106—1116no—
239#106C22×D1118yes—
240#106C22×D1118yes—
241#97—118no—
242C4×C8—118no—
243C2×C11—24no—
244C2×C11#316314yescomplemented
245C2×C11C22×C4⋊Q811yescharacteristic
246C2×C11C2×#57712yes—
247C24D4×D1111yescharacteristic
248C2×Q8—2216no—
249C2×Q8—888no—
250C22×C4—24no—
251C22×C4—28no—
252C22×C4—84no—
253C22×C4—114no—
254C22×C4—222no—
255C22×C4—222no—
256C22×C4C2×Dic2214yes—
257C22×C4D4×D1112yes—
258C22×C4D4×D1111yescharacteristic
259C22×C4Q8×D1114yes—
260C22×C4C23×D1112yes—
261C22×C4C23×D1111yescharacteristic
262M16—1116no—
263C2×C8—118no—
264C2×C8—114no—
265C2×C8C2×Dic2214yes—
266C2×C8C2×Dic2214yes—
267C2×C8C2×Dic22116yescomplemented
268C2×C8C23×D1112yes—
269C2×C8C23×D1112yes—
270C4⋊C4—24no—
271C4⋊C4—28no—
272C4⋊C4—118no—
273C4⋊C4—114no—
274C4⋊C4—114no—
275C4⋊C4—2216no—
276C4⋊C4—2216no—
277C4⋊C4—2216no—
278C4⋊C4—222no—
279C4⋊C4—222no—
280C4⋊C4C23×D1118yes—
281C22⋊C4—118no—
282C22⋊C4—228no—
283C42—114no—
284C42—114no—
285C42—228no—
286C11C2×#316311yescharacteristic, complemented, Sylow
287C23—24no—
288C23#6694114yes—
289C23C2×D4×D1112yes—
290C23C2×D4×D1111yescharacteristic
291Q8—8816no—
292C2×C4—28no—
293C2×C4—48no—
294C2×C4—88no—
295C2×C4—118no—
296C2×C4—228no—
297C2×C4—224no—
298C2×C4—224no—
299C2×C4—444no—
300C2×C4—444no—
301C2×C4#6694118yes—
302C2×C4#6694114yes—
303C2×C4C22×Dic2212yes—
304C2×C4C22×Dic2214yes—
305C2×C4C2×D4×D1111yescharacteristic
306C2×C4C2×D4×D1112yes—
307C2×C4C2×Q8×D1112yes—
308C2×C4C2×Q8×D1114yes—
309C2×C4C24×D1111yescharacteristic
310C8—118no—
311C8C22×Dic2214yes—
312C8C22×Dic2214yes—
313C22—28no—
314C22—24no—
315C22C2×#6694114yes—
316C22C2×#6694112yes—
317C22#1062329314yes—
318C22C22×D4×D1111yescharacteristic
319C4—48no—
320C4—228no—
321C4—444no—
322C4—444no—
323C4C2×#6694112yes—
324C4C2×#6694114yes—
325C4C23×Dic2211yescharacteristic
326C4C22×Q8×D1111yescharacteristic
327C2—24no—
328C2#1307914414yesdirect product factor
329C2C22×#6694111yescharacteristic
330C2C2×#1062329312yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#106C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC22×#106D11
hypocenterC11C2×#3163
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13079144C2direct (N × H)
3. C2×#10622469C2semidirect
4. C2×#10622471C2semidirect
5. C2×#10622468C2semidirect
35. #10622471C22semidirect
36. #10622469C22semidirect
37. #10622468C22semidirect
41. C22×C8×C11Q8semidirect
64. C2×#4318Q8semidirect
100. C2×C8×C11C2×Q8semidirect
119. #4318C2×Q8semidirect
205. C22×C8Dic22semidirect
244. C2×C11#3163semidirect
267. C2×C8C2×Dic22semidirect
286. C11C2×#3163semidirect
328. C2#13079144direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106230312
#130791442
C2×#106224692
C2×#106224712
C2×#106224682
C2×#106225772
C2×#106227192
C2×#106227142
C22×C11×#1062
C2×#316311